Abstract : The study concerns a numerical investigation of incompressible flow in the entrance region of a concentric annulus with the inside cylinder rotating. The elliptical Navier Stokes equations are reduced to parabolic equations with the aid of straining coordinates and assuming high leakage Reynolds number. The system of equations is numerically integrated by the classical marching techniques which were developed for parabolic systems. The nondimensional mathematical system of equations is solved by the classical central difference Crank-Nicholson implicit scheme. The z and phi momentum equations and the energy equation are put in the form of a tri-diagonal matrix and are solved by the Gaussian reduction method. The program for the solution of velocity components was run without specifying any value for the Reynolds number. (Modified author abstract)